xoEPC - Jan Mendling

3.4. EPC Semantics 75
(a) (b)
(c) (d)
d
d d d
Figure 3.16: Transition Relation for Negative Token Propagation
Phase 4: Positive Token Propagation
The transition relation for positive token propagation specifies firing rules that consume
negative and positive tokens from the input arcs of a node to produce positive tokens on
its output arcs. Figure 3.17 gives a respective illustration. Rules (a) and (b) show that
functions and events consume positive tokens from the input arc and propagate them to
the output arc. Furthermore, and this holds true for all rules, consuming a positive token
from an arc implies setting this arc to a dead context status. Rules (c) and (d) illustrate
that AND-splits consume one positive token and produce one on each output arc, while
AND-joins synchronize positive tokens on all input arcs to produce one on the output arc.
Rule (e) depicts the fact that XOR-splits forward positive tokens to one of their output
arcs. In contrast to the Boolean net formalization, they do not produce negative tokens,
but a dead context on the output arcs which do not receive the token. Correspondingly,
XOR-joins (f) propagate each incoming positive token to the output arc, no matter what
the context or the state of the other input arcs is. If there are negative tokens on the
incoming arcs, they are consumed. The OR-split (g) produces positive tokens on those
output arcs that have to be executed and negative tokens on those that are ignored. Note
that the OR-join is the only construct that may introduce negative tokens (apart from start
events that hold a negative token in the initial marking). Rule (h) shows that on OR-join
can only fire either if it has full information about the state of its input arcs (i.e., each
input has a positive or a negative token) or all arcs that do not hold a token are in a dead
context. Finally, in all rules, each output arc that receives a negative token is set to a dead
d